The Application of Neutral Landscape Models in Conservation Biology

Neutral landscape models, derived from percolation theory in the field of landscape ecology, are grid-based maps in which complex habitat distributions are generated by random or fractal algorithms. This grid-based representation of landscape structure is compatible with the raster-based format of geographical information systems (GIS), which facilitates comparisons between theoretical and real landscapes. Neutral landscape models permit the identification of critical thresholds in connectivity, which can be used to predict when landscapes will become fragmented. The coupling of neutral landscape models with generalized population models, such as metapopulation theory, provides a null model for generating predictions about population dynamics in fragmented landscapes. Neutral landscape models can contribute to the following applications in conservation: (1) incorporation of complex spatial patterns in (meta)population models; (2) identification of species' perceptions of landscape structure; (3) determination of landscape connectivity; (4) evaluation of the consequences of habitat fragmentation for population subdivision; (5) identification of the domain of metapopulation dynamics; (6) prediction of the occurrence of extinction thresholds; ( 7) determination of the genetic consequences of habitat fragmentation; and (8) reserve design and ecosystem management. This generalized, spatially explicit framework bridges the gap between spatially implicit, patch-based models and spatially realistic GIS applications which are usually parameterized for a single species in a specific landscape. Development of a generalized, spatially explicit framework is essential in conservation biology because we will not be able to develop individual models for every species of management concern.     

Designing a Conservation Landscape for Tigers in Human-Dominated Environments

Abstract:  Wildlife populations in small, isolated reserves face genetic and demographic threats to their survival. To increase the probability of long-term persistence, biologists promote metapopulation management, in which breeding subpopulations are protected as source pools. Animals that disperse from the source pools increase the probability of persistence of the metapopulation across the greater landscape. We used a geographic information system (GIS)–based, cost-distance model to design a conservation landscape along the Himalayan foothills for managing a metapopulation of Asia's largest predator, the tiger ( Panthera tigris ). The model is based on data from 30 years of field research on tigers, recent satellite imagery, and a decade of buffer-zone restoration in this region. We used the model to (1) identify potential dispersal corridors for tigers; (2) identify strategic transit refuges; and (3) make recommendations for off-reserve land management and restoration to enhance the potential of corridors for tigers. This tool can aid the design of conservation landscapes for other endangered, wide-ranging species in human-dominated environments.     

Comparison of Two Types of Metapopulation Models in Real and Artificial Landscapes

Abstract: Application of metapopulation models is becoming increasingly widespread in the conservation of species in fragmented landscapes. We provide one of the first detailed comparisons of two of the most common modeling techniques, incidence function models and stage-based matrix models, and test their accuracy in predicting patch occupancy for a real metapopulation. We measured patch occupancies and demographic rates for regional populations of the Florida scrub lizard (   Sceloporus woodi ) and compared the observed occupancies with those predicted by each model. Both modeling strategies predicted patch occupancies with good accuracy ( 77–80%) and gave similar results when we compared hypothetical management scenarios involving removal of key habitat patches and degradation of habitat quality. To compare the two modeling approaches over a broader set of conditions, we simulated metapopulation dynamics for 150 artificial landscapes composed of equal-sized patches (2–1024 ha) spaced at equal distances (50–750 m). Differences in predicted patch occupancy were small to moderate (<20%) for about 74% of all simulations, but 22% of the landscapes had differences openface> 50%. Incidence function models and stage-based matrix models differ in their approaches, assumptions, and requirements for empirical data, and our findings provide evidence that the two models can produce different results. We encourage researchers to use both techniques and further examine potential differences in model output. The feasibility of obtaining data for population modeling varies widely among species and limits the modeling approaches appropriate for each species. Understanding different modeling approaches will become increasingly important as conservation programs undertake the challenge of managing for multiple species in a landscape context.     

Influence of Landscape Elements in Riparian Buffers on the Conservation of Semiaquatic Amphibians

Abstract:  Studies on riparian buffers have usually focused on the amount of land needed as habitat for the terrestrial life stages of semiaquatic species. Nevertheless, the landscape surrounding wetlands is also important for other key processes, such as dispersal and the dynamics of metapopulations. Multiple elements that influence these processes should therefore be considered in the delineation of buffers. We analyzed landscape elements (forest cover, density of roads, and hydrographic network) in concentric buffers to evaluate the scale at which they influence stream amphibians in 77 distinct landscapes. To evaluate whether our results could be generalized to other contexts, we determined whether they were consistent across the study areas. Amphibians required buffers of 100–400 m of suitable terrestrial habitat, but interspecific differences in the amount of habitat were large. The presence of amphibians was related to roads and the hydrographic network at larger spatial scales (300–1500 m), which suggests that wider buffers are needed with these elements. This pattern probably arose because these elements influence dispersal and metapopulation persistence, processes that occur at large spatial scales. Furthermore, in some cases, analyses performed on different sets of landscapes provided different results, which suggests caution should be used when conservation recommendations are applied to disparate areas. Establishment of riparian buffers should not be focused only on riparian habitat, but should take a landscape perspective because semiaquatic species use multiple elements for different functions. This approach can be complex because different landscape elements require different spatial extents. Nevertheless, a shift of attention toward the management of different elements at multiple spatial scales is necessary for the long-term persistence of populations.     

Utility of Dynamic-Landscape Metapopulation Models for Sustainable Forest Management

Abstract:  We evaluated the utility of combining metapopulation models with landscape-level forest-dynamics models to assess the sustainability of forest management practices. We used the Brown Creeper ( Certhia americana ) in the boreal forests of northern Ontario as a case study. We selected the Brown Creeper as a potential indicator of sustainability because it is relatively common in the region but is dependent on snags and old trees for nesting and foraging; hence, it may be sensitive to timber harvesting. For the modeling we used RAMAS Landscape, a software package that integrates RAMAS GIS, population-modeling software, and LANDIS, forest-dynamics modeling software. Predictions about the future floristic composition and structure of the landscape under a variety of management and natural disturbance scenarios were derived using LANDIS. We modeled eight alternative forest management scenarios, ranging in intensity from no timber harvesting and a natural fire regime to intensive timber harvesting with salvage logging after fire. We predicted the response of the Brown Creeper metapopulation over a 160-year period and used future population size and expected minimum population size to compare the sustainability of the various management scenarios. The modeling methods were easy to apply and model predictions were sensitive to the differences among management scenarios, indicating that these methods may be useful for assessing and ranking the sustainability of forest management options. Primary concerns about the method are the practical difficulties associated with incorporating fire stochasticity in prediction uncertainty and the number of model assumptions that must be made and tested with sensitivity analysis. We wrote new software to help quantify the contribution of landscape stochasticity to model prediction uncertainty.     

Appreciating Ecological Complexity: Habitat Contours as a Conceptual Landscape Model

Abstract:  Organisms respond to their surroundings at multiple spatial scales, and different organisms respond differently to the same environment. Existing landscape models, such as the "fragmentation model" (or patch-matrix-corridor model) and the "variegation model," can be limited in their ability to explain complex patterns for different species and across multiple scales. An alternative approach is to conceptualize landscapes as overlaid species-specific habitat contour maps. Key characteristics of this approach are that different species may respond differently to the same environmental conditions and at different spatial scales. Although similar approaches are being used in ecological modeling, there is much room for habitat contours as a useful conceptual tool. By providing an alternative view of landscapes, a contour model may stimulate more field investigations stratified on the basis of ecological variables other than human-defined patches and patch boundaries. A conceptual model of habitat contours may also help to communicate ecological complexity to land managers. Finally, by incorporating additional ecological complexity, a conceptual model based on habitat contours may help to bridge the perceived gap between pattern and process in landscape ecology. Habitat contours do not preclude the use of existing landscape models and should be seen as a complementary approach most suited to heterogeneous human-modified landscapes.     

Spatial occurrence of a habitat-tracking saproxylic beetle inhabiting a managed forest landscape.

Because of the dynamic nature of many managed habitats, proper evaluation of conservation efforts calls for models that take into account both spatial and temporal habitat dynamics. We develop a metapopulation model for successional-type systems, in which habitat quality changes over time in a predictable fashion. The occupancy and recruitment of the predatory saproxylic (dependent on dead wood) beetle Harminius undulatus was studied in a managed boreal forest landscape, covering 24,449 ha, in central Sweden. In a first step, we analyzed the beetle's occupancy pattern in relation to stand characteristics, and the amounts of present and past habitat in the surrounding landscape. Managed forest is suitable habitat when > or =60 years old, and immediately after cutting, but not between the ages of 10 and 60 years. The observed occupancy of H. undulatus was positively correlated with the stand's age as habitat. We used a metapopulation model to predict the current probability of occurrence in each forest stand, given the spatiotemporal distribution of suitable forest stands during the last 50 years. Metapopulation parameters were estimated by matching predicted spatial distributions with observed spatial distributions. The model predicted observed spatial distributions better than a similar model that assumed constant habitat quality of each forest stand. Thus, metapopulation models for successional-type systems, such as dead wood dependent organisms in managed forest landscapes, should include habitat dynamics. An estimated 82% of the landscape-wide recruitment took place in managed stands, which covered 87% of the forest area, in comparison with 18% in unmanaged stands, which covered 13% of the forest area. Among the managed stand types, > or =60-year-old stands and 3-7-year-old clear-cuttings contributed to 79% of the total recruitment while 8-59-year-old stands only contributed 3%. The results suggest the following guidelines to improve conditions for H. undulatus and other species with similar habitat requirements: (1) the proportion of the landscape constituted by younger stands should not be allowed to grow too large, (2) the rotation period of managed stands should not be allowed to be too short, and (3) dead wood should be retained and created at final cutting.     

Incorporating landscape stochasticity into population viability analysis.

The importance of incorporating landscape dynamics into population viability analysis (PVA) has previously been acknowledged, but the need to repeat the landscape generation process to encapsulate landscape stochasticity in model outputs has largely been overlooked. Reasons for this are that (1) there is presently no means for quantifying the relative effects of landscape stochasticity and population stochasticity on model outputs, and therefore no means for determining how to allocate simulation time optimally between the two; and (2) the process of generating multiple landscapes to incorporate landscape stochasticity is tedious and user-intensive with current PVA software. Here we demonstrate that landscape stochasticity can be an important source of variance in model outputs. We solve the technical problems with incorporating landscape stochasticity by deriving a formula that gives the optimal ratio of population simulations to landscape simulations for a given model, and by providing a computer program that incorporates the formula and automates multiple landscape generation in a dynamic landscape metapopulation (DLMP) model. Using a case study of a bird population, we produce estimates of DLMP model output parameters that are up to four times more precise than those estimated from a single landscape in the same amount of total simulation time. We use the DLMP modeling software RAMAS Landscape to run the landscape and metapopulation models, though our method is general and could be applied to any PVA platform. The results of this study should motivate DLMP modelers to consider landscape stochasticity in their analyses.     

Metapopulation dynamics in the butterfly Hipparchia semele changed decades before occupancy declined in The Netherlands

The survival of many species in human-dominated, fragmented landscapes depends on metapopulation dynamics, i.e., on a dynamic equilibrium of extinctions and colonizations in patches of suitable habitat. To understand and predict distributional changes, knowledge of these dynamics can be essential, and for this, metapopulation studies are preferably based on long-time-series data from many sites. Alas, such data are very scarce. An alternative is to use opportunistic data (i.e., collected without applying standardized field methods), but these data suffer from large variations in field methods and search intensity between sites and years. Dynamic site-occupancy models offer a general approach to adjust for variable survey effort. These models extend classical metapopulation models to account for imperfect detection of species and yield estimates of the probabilities of occupancy, colonization, and survival of species at sites. By accounting for detection, they fully correct for among-year variability in search effort. As an illustration, we fitted a dynamic site-occupancy model to 60 years of presence-absence data (more precisely, detection-nondetection) of the heathland butterfly Hipparchia semele in The Netherlands. Detection records were obtained from a database containing volunteer-based data from 1950-2009, and nondetection records were deduced from database records of other butterfly species. Our model revealed that metapopulation dynamics of Hipparchia had changed decades before the species' distribution began to contract. Colonization probability had already started to decline from 1950 onward, but this was counterbalanced by an increase in the survival of existing populations, the result of which was a stable distribution. Only from 1990 onward was survival not sufficient to compensate for the further decrease of colonization, and occupancy started to decline. Hence, it appears that factors acting many decades ago triggered a change in the metapopulation dynamics of this species, which ultimately led to a severe decline in occupancy that only became apparent much later. Our study emphasizes the importance of knowledge of changes in survival and colonization of species in modern landscapes over a very long time scale. It also demonstrates the power of site-occupancy modeling to obtain important population dynamics information from databases containing opportunistic sighting records.     

Linking life history to landscape for threatened species conservation in a multiuse region

Landscape-scale conservation that considers metapopulation dynamics will be essential for preventing declines of species facing multiple threats to their survival. Toward this end, we developed a novel approach that combines occurrence records, spatial–environmental data, and genetic information to model habitat, connectivity, and patterns of genetic structure and link spatial attributes to underlying ecological mechanisms. Using the threatened northern quoll (Dasyurus hallucatus) as a case study, we applied this approach to address the need for conservation decision-making tools that promote resilient metapopulations of this threatened species in the Pilbara, Western Australia, a multiuse landscape that is a hotspot for biodiversity and mining. Habitat and connectivity were predicted by different landscape characteristics. Whereas habitat suitability was overwhelmingly driven by terrain ruggedness, dispersal was facilitated by proximity to watercourses. Although there is limited evidence for major physical barriers in the Pilbara, areas with high silt and clay content (i.e., alluvial and hardpan plains) showed high resistance to dispersal. Climate subtlety shaped distributions and patterns of genetic turnover, suggesting the potential for local adaptation. By understanding these spatial–environmental associations and linking them to life-history and metapopulation dynamics, we highlight opportunities to provide targeted species management. To support this, we have created habitat, connectivity, and genetic uniqueness maps for conservation decision-making in the region. These tools have the potential to provide a more holistic approach to conservation in multiuse landscapes globally.     

Patch Occupancy and Potential Metapopulation Dynamics of Three Forest Mammals in Fragmented Afromontane Forest in South Africa

Abstract: We investigated the persistence of three medium-sized (2–9 kg), rare forest mammals in the fragmented mist-belt Podocarpus forests of the midlands of KwaZulu-Natal Province, South Africa. We recorded patch occupancy of blue duiker (   Philantomba monticola ), tree hyrax (   Dendrohyrax arboreus ), and samango monkey ( Cercopithecus mitis labiatus ) in 199 forest patches. Their rarity is ascribed to the fragmentation and destruction of their forest habitat. Incidence functions, derived from presence and absence data, were formulated as generalized linear models, and environmental effects were included in the fitted logistic models. The small and mostly solitary hyrax and duiker persisted in smaller patches than the large and social monkey. Although this result follows expectations based on relative home-range sizes of each species, the incidence probability of the samango monkey was invariant with increasing isolation, whereas a gradual decrease with increasing isolation was observed for the hyrax and duiker. Group dynamics may inhibit dispersal and increase the isolation effect in social species such as samango monkeys. A mainland-island metapopulation model adequately describes patterns of patch occupancy by the hyrax and duiker, but the monkeys' poor dispersal ability and obvious area-dependent extirpation suggest that they exist in transient, nonequilibrium (declining) metapopulations. Through identification of large forest patches for careful protection and management, the survival of all three species—especially the monkey—could be prolonged. Because no functional metapopulation may exist for the monkey, however, this is an emergency measure. For the duiker and hyrax, larger patches should form part of a network of smaller and closer patches in a natural matrix.     

Nesting Success of Neotropical Migrant Songbirds in a Highly Fragmented Landscape

Abstract: Small forests in agricultural landscapes are generally thought to be population sinks where the nesting success of Neotropical migrant songbirds is too low to sustain populations. In 1996 and 1997, we assessed the nesting success and productivity of Wood Thrushes (  Hylocichla mustelina ) and Rose-breasted Grosbeaks (  Pheucticus ludovicianus ) in the Region of Waterloo, a highly fragmented agricultural landscape with 14% forest cover in southwestern Ontario. We located 154 Wood Thrush nests and 63 Rose-breasted Grosbeak nests in 26 small forest fragments (3–14 ha) and 15 large fragments (26–140 ha). We used the Mayfield method to determine nesting success. Across all sites nesting success was 51% for Wood Thrushes and 46% for Rose-breasted Grosbeaks. Nesting success and productivity rates were used in a simple population growth model that suggested that the Wood Thrushes but not the Rose-breasted Grosbeaks were a self-sustaining population. Forest size and distance of nests to the nearest forest edge (measured in five distance classes ranging from 0 to over 100 m) did not significantly affect the nesting success or productivity of either species. Brown-headed Cowbirds (   Molothrus ater ) parasitized 47% of all Wood Thrush nests and 10% of all Rose-breasted Grosbeak nests; parasitism significantly reduced Wood Thrush productivity but not that of Rose-breasted Grosbeaks. Our findings challenge the prevailing notion that small woodlots in a farmed landscape are invariably habitat sinks and offer additional incentive for habitat protection in settled landscapes where small forest fragments are often all that remain for conservation purposes.     

Landscape history, fragmentation, and patch occupancy: models for a forest bird with limited dispersal.

We developed and tested patch occupancy models for an endemic understory bird with limited dispersal ability, the Chucao Tapaculo (Scelorchilus rubecula), in two South American temperate rain forest landscapes that differed in levels and duration of forest loss. We assessed cover changes since 1961 in each landscape and surveyed patches for Chucao Tapaculo occupancy. We then developed incidence-based predictive models independently for each landscape and tested each model reciprocally in the alternative study area. We thereby assessed the domain of model applicability and identified those predictor variables with general effects and those that varied between the two landscapes. The two models were consistent regarding variable selection, and predictive accuracy of each model was high in the landscape where training data were collected. However, the models differed substantially in the magnitudes of effects related to patch size, with larger unoccupied patches observed in the landscape with the more advanced stage of fragmentation. Due to this discrepancy, each model performed poorly when applied to the alternative landscape, potentially reflecting the contrasting stages of habitat loss. Although it was impossible to dissociate effects of level and duration of forest loss, we viewed the landscapes as representing two extremes along a continuum of fragmentation, providing insights into potential trajectories for portions of the biome where deforestation is occurring. Further, our data suggest that static equilibrium models developed from distribution patterns in recently fragmented landscapes may overestimate persistence when used as a forecasting tool, or when extrapolated to alternative landscapes where fragmentation is more advanced. Thus, we suggest that landscapes used as standards for model building should be selected with caution. We recommend that distribution patterns be obtained from landscapes where fragmentation is advanced, preferably with histories of fragmentation long enough that time-delayed extinctions already would have occurred.     

Extraterritorial Movements of a Forest Songbird in a Fragmented Landscape

Abstract: Forest isolation resulting from fragmentation is thought to impede the movement of forest songbirds. Because of the difficulty of tracking birds continuously, however, few data exist documenting the influence of isolation and landscape features on avian movements. During the breeding season, male Hooded Warblers (    Wilsonia citrina ) leave their small (<2.5 ha), isolated forest patches to travel between forest fragments. We documented a total of 106 forays (  n = 20 males) and found that individuals traveled up to 2.5 km away from their resident forest patch, primarily to solicit covert extra-pair copulations. Forays occurred despite the absence of forested corridors connecting fragments; even when corridors were present, males most often chose to fly directly across open fields. Resident patch size and distance to forests visited were not correlated with the frequency of forays. The maximum distance males flew over open fields did not exceed 465 m, and longer distances likely inhibit males from traveling outside their woodlots. If territorial establishment depends on the availability of extra-pair partners, then higher degrees of isolation between forests could explain why some species avoid settling in extremely fragmented landscapes. Conservation efforts should limit isolation between forest stands, thereby preserving the ability of animals to move within fragmented landscapes during the breeding season.     

Avifaunal Use of Wooded Streets in an Urban Landscape

Abstract: Birds in urban landscapes primarily occupy parks (  forest fragments), wooded streets ( linear strips connecting fragments), or the urban matrix. I studied the effects of street location in the landscape, vegetation structure, and human disturbance ( pedestrian and automobile load) within wooded streets on bird species richness, temporal persistence, and density of feeding and nesting guilds, and on the probability of street occupation by individual species in Madrid during two consecutive breeding seasons. The number of species recorded increased from the least suitable (control streets without vegetation) to the most suitable habitats (urban parks), with wooded streets being intermediate landscape elements. Fourteen species, belonging to four of the eight guilds identified in this system, were recorded in wooded streets in both years. Streets that connected urban parks, along with vegetation structure, positively influenced the number of species within wooded streets, species persistence, guild density, and probability of occupation of streets by individual species. Human disturbance exerted a negative influence on the same variables. Wooded streets potentially could function as corridors, allowing certain species—particularly those feeding on the ground and breeding in trees or tree holes—to fare well by supporting alternative habitat for feeding and nesting. Local improvements in corridor quality, through increased vegetation complexity and reduced human disturbance, could exert a positive influence on the regional connectivity of the system. Because of differential use of corridors by species with different habitat requirements, however, corridor implementation should also take into account the target species of management.     

The Sensitivity of Population Viability Analysis to Uncertainty about Habitat Requirements: Implications for the Management of the Endangered Southern Brown Bandicoot

Abstract:  Whenever population viability analysis (PVA) models are built to help guide decisions about the management of rare and threatened species, an important component of model building is the specification of a habitat model describing how a species is related to landscape or bioclimatic variables. Model-selection uncertainty may arise because there is often a great deal of ambiguity about which habitat model structure best approximates the true underlying biological processes. The standard approach to incorporate habitat models into PVA is to assume the best habitat model is correct, ignoring habitat-model uncertainty and alternative model structures that may lead to quantitatively different conclusions and management recommendations. Here we provide the first detailed examination of the influence of habitat-model uncertainty on the ranking of management scenarios from a PVA model. We evaluated and ranked 6 management scenarios for the endangered southern brown bandicoot ( Isoodon obesulus ) with PVA models, each derived from plausible competing habitat models developed with logistic regression. The ranking of management scenarios was sensitive to the choice of the habitat model used in PVA predictions. Our results demonstrate the need to incorporate methods into PVA that better account for model uncertainty and highlight the sensitivity of PVA to decisions made during model building. We recommend that researchers search for and consider a range of habitat models when undertaking model-based decision making and suggest that routine sensitivity analyses should be expanded to include an analysis of the impact of habitat-model uncertainty and assumptions.     

Managing Boreal Forest Landscapes for Flying Squirrels

Abstract: Flying squirrel (Pteromys volans) populations have declined severely during the past few decades, and the species has become a focal species in forest management and the conservation debate in Finland. We compared landscape structure around known flying squirrel home ranges with randomly chosen forest sites to determine which landscape patterns characterize the areas occupied by the species in northern Finland. We sought to identify the key characteristics of the landscape that support the remaining flying squirrel populations. We analyzed landscape structure within circular areas with 1- and 3-km radii around 63 forest sites occupied by flying squirrels, and around 96 random sites. We applied stepwise analysis of the landscape structure where landscapes were built up step-by-step by adding patch types in order of their suitability for the flying squirrel. The land-use and forest-resource data for the analysis were derived from multisource national forest inventory and imported to a geographical information system. Landscape patch types were divided into three suitability categories: breeding habitat (mixed spruce-deciduous forests); dispersal habitat ( pine and young forests); and unsuitable habitat ( young sapling stands, open habitats, water). Flying squirrel landscapes contained more suitable breeding habitat patches and were better connected by dispersal habitats than random landscapes. Our results suggest that for the persistence of the flying squirrel, forest managers should 1) maintain a deciduous mixture, particularly in spruce-dominated forests; 2) maintain physical connectivity between optimal breeding habitats; and 3) impose coarse-grained structures on northeastern Finnish landscapes at current levels of habitat availability.     

Long-Term Landscape Change and Bird Abundance in Amazonian Rainforest Fragments

Abstract:  The rainforests of the Amazon basin are being cut by humans at a rate >20,000 km²/year, leading to smaller and more isolated patches of forest, with remaining fragments often in the range of 1–100 ha. We analyzed samples of understory birds collected over 20 years from a standardized mist-netting program in 1– to 100-ha rainforest fragments in a dynamic Amazonian landscape near Manaus, Brazil. Across bird guilds, the condition of second growth immediately surrounding fragments was often as important as fragment size or local forest cover in explaining variation in abundance. Some fragments surrounded by 100 m of open pasture showed reductions in insectivorous bird abundance of over 95%, even in landscapes dominated by continuous forest and old second growth. These extreme reductions may be typical throughout Amazonia in small (≤10 ha), isolated fragments of rainforest. Abundance for some guilds returned to preisolation levels in 10- and 100-ha fragments connected to continuous forest by 20-year-old second growth. Our results show that the consequences of Amazonian forest loss cannot be accurately described without explicit consideration of vegetation dynamics in matrix habitat. Any dichotomous classification of the landscape into "forest" and "nonforest" misses essential information about the matrix.